Write the number in a place-value chart. Read the value of the 8 native the chart.

You are watching: How many thousandths are in one hundredth

Answer In the number 4,279.386, the 8 is in the percentage percent place.


What is the ar value the the 7 in 324.2671?

A) thousands

B) thousandths

C) hundreds

D) hundredths


A) thousands

Incorrect. The digit 7 is to the appropriate of the decimal point, which way that it is much less than one and also on the th side. The exactly answer is thousandths.

B) thousandths

Correct. The digit 7 is 3 decimal locations to the appropriate of the decimal point, which method that that is in the thousandths place.

C) hundreds

Incorrect. The digit 7 is three decimal areas to the ideal of the decimal point, which means that that is in the thousandths place.

D) hundredths

Incorrect. The digit 7 is 3 decimal places to the best of the decimal point, which way that it is in the thousandths place.

Reading Decimals


The easiest method to check out a decimal number is to review the decimal portion part together a fraction. (Don’t simplify the fraction though.) suppose you have actually 0.4 grams of yogurt in a cup. You would certainly say, “4 tenths of a gram of yogurt,” as the 4 is in the tenths place.

Note that the denominator that the fraction written in fraction form is constantly a power of ten, and also the number of zeros in the denominator is the same as the variety of decimal locations to the best of the decimal point. See the examples in the table below for additional guidance.


Decimal Notation

Fraction Notation

Word Form

0.5

five tenths

0.34

*

thirty-four hundredths

0.896

*

eight hundreds ninety-six thousandths


Notice the 0.5 has actually one decimal place. Its tantamount fraction,

*
, has actually a denominator the 10—which is 1 followed by one zero. In general, once you space converting decimal to fractions, the denominator is always 1, followed by the variety of zeros that correspond to the number of decimal areas in the original number.

Another means to identify which number to location in the denominator is to usage the ar value the the critical digit there is no the “ths” part. Because that example, if the number is 1.458, the 8 is in the thousandths place. Take away the “ths” and also you have a thousand, so the number is written as

*
.

 


Example

Problem

Write 0.68 in indigenous form.

0.68 =

*
 = sixty-eight hundredths

Note the the number is check out as a fraction.

Also note that the denominator has 2 zeros, the exact same as the number of decimal areas in the initial number.

Answer The number 0.68 in word form is sixty-eight hundredths.


Recall that a An expression in i beg your pardon a whole number is merged with a suitable fraction. For example 5

*
 

is a mixed number.


")">mixed number
is a combination of a whole number and also a fraction. In the situation of a decimal, a blended number is additionally a combination of a whole number and a fraction, whereby the portion is composed as a decimal fraction.

To read blended numbers, to speak the whole number part, words “and” (representing the decimal point), and also the number come the appropriate of the decimal point, adhered to by the name and the place value that the last digit. You deserve to see this demonstrated in the chart below, in i m sorry the critical digit is in the ten thousandths place.

*

Another way to think about this is with money. Suppose you salary $15,264.25 because that a car. You would review this as fifteen thousand, two hundred sixty-four dollars and twenty-five cents. In this case, the “cents” method “hundredths that a dollar,” so this is the very same as saying fifteen thousand, 2 hundred sixty-four and twenty-five hundredths. A couple of more instances are displayed in the table below.


Decimal Notation

Fraction Notation

Word Form

9.4

*

Nine and four tenths

87.49

*

Eighty-seven and also forty-nine hundredths

594.236

*

Five hundred ninety-four and also two hundreds thirty-six thousandths


Example

Problem

Write 4.379 in indigenous form.

4.379 =

*
= four and three hundreds seventy-nine thousandths

The decimal fraction is review as a fraction.

Note that the denominator has 3 zeros, the exact same as the variety of decimal locations in the initial number.

Answer The number 4.379 in word form is four and also three hundreds seventy-nine thousandths.


Write 2.364 in indigenous form.

A) two and also three hundred sixty-four hundredths

B) two and also three hundred sixty-four thousandths

C) 2 thousand three hundred sixty-four

D) three hundred sixty-four tenths and two


Show/Hide Answer

A) two and also three hundreds sixty-four hundredths

Incorrect. You indicated the not correct decimal ar in her answer. The exactly answer is two and three hundred sixty-four thousandths.

B) two and also three hundred sixty-four thousandths

Correct. 2.364 is the same as

*
, so in enhancement to the entirety number 2, you have three hundred sixty-four thousandths.

C) two thousand 3 hundred sixty-four

Incorrect. You ignored the decimal point. The exactly answer is a decimal; in this case, two and also three hundreds sixty-four thousandths.

D) three hundred sixty-four tenths and two

Incorrect. You indicated the dorn decimal place in your answer, and also the whole number component should it is in mentioned prior to the decimal part. The exactly answer is two and three hundreds sixty-four thousandths.

Writing decimals as simplified Fractions


As you have seen above, every decimal deserve to be written as a fraction. To convert a decimal come a fraction, place the number ~ the decimal suggest in the numerator of the portion and place the number 10, 100, or 1,000, or an additional power that 10 in the denominator. Because that example, 0.5 would be composed as . You’ll notification that this portion can be further simplified, as  reduces to

*
, which is the last answer.

Let’s get an ext familiar with this relationship in between decimal places and zeros in the denominator by feather at numerous examples. Notification that in every example, the number of decimal locations is different.


Example

Problem

Write 0.6 as a simplified fraction.

0.6 =

*

*

The critical decimal place is tenths, so use 10 for your denominator. The number of zeros in the denominator is constantly the very same as the number of decimal areas in the original decimal.

Simplify the fraction.

Answer 0.6 =


Let’s look at at an instance in i m sorry a number v two decimal locations is written as a fraction.


Example

Problem

Write 0.64 as a simplified fraction.

0.64 =

*

*

The critical decimal place is hundredths, so usage 100 for her denominator. The variety of zeros in the denominator is always the very same as the number of decimal places in the original decimal.

Simplify the fraction.

Answer 0.64 =

*


Now, examine how this is done in the example below using a decimal v digits in three decimal places.

 


Example

Problem

Write 0.645 as a streamlined fraction.

0.645 =

*

*

Note the there are 3 zeros in the denominator, i beg your pardon is the exact same as the variety of decimal areas in the original decimal.

Simplify the fraction.

Answer 0.645 =

*


You have the right to write a fraction as a decimal even when there room zeros come the ideal of the decimal point. Below is an instance in which the just digit better than zero is in the thousandths place.


Example

Problem

Write 0.007 as a streamlined fraction.

0.007 =  

Note the 7 is in the thousandths place, therefore you write 1,000 in the denominator. The number of zeros in the denominator is always the very same as the variety of decimal places in the initial decimal.

The portion cannot be streamlined further.

Answer 0.007 =


When composing decimals higher than 1, you only require to readjust the decimal part to a portion and save the totality number part. Because that example, 6.35 can be composed as 6

*
.

 


Example

Problem

Write 8.65 as a simplified blended fraction.

8.65 = 8

*
 = 8
*

Rewrite 0.65 as

Note the the variety of zeros in the denominator is two, i m sorry is the same as the number of decimal locations in the original decimal.

Then simplify

by separating numerator and denominator by 5.

Answer 8.65 =

*


Write 0.25 as a fraction.

A)

B)

C)

D)


Show/Hide Answer

A)

Incorrect. Girlfriend may have actually put the number from the tenths ar in the numerator, and also the number from the hundredths place in the denominator. The correct answer is .

B)

Correct. The number 0.25 have the right to be composed as

*
, i m sorry reduces come .

C)

Incorrect. You probably puzzled the numerator and the denominator. The exactly answer is .

D)

Incorrect. You may have put the digit from the tenths ar in the denominator, and the number from the hundredths place in the numerator. The exactly answer is .

Writing Fractions together Decimals


Just as you deserve to write a decimal together a fraction, every portion can be written as a decimal. To create a portion as a decimal, divide the numerator (top) of the fraction by the denominator (bottom) of the fraction. Use long division, if necessary, and also note wherein to location the decimal point in your answer. Because that example, to write  as a decimal, division 3 by 5, which will an outcome in 0.6.


Example

Problem

Write

*
 as a decimal.

*

−1 0

0

Using long division, you deserve to see that dividing 1 by 2 results in 0.5.

Answer

*
= 0.5


Note that you could additionally have thought around the trouble like this:

*
, and then addressed for ?. One method to think around this problem is that 10 is 5 times higher than 2, for this reason ? will need to be five times higher than 1. What number is 5 times higher than 1? five is, therefore the solution is
*
.

Now look in ~ a more complex example, wherein the final digit that the answer is in the thousandths place.


Example

Problem

Write

*
as a decimal.

*

−2 4

60

− 56

40

− 40

0

Using lengthy division, you deserve to see that separating 3 through 8 outcomes in 0.375.

Answer

*
 = 0.375


Converting from fractions to decimals sometimes results in answers with decimal numbers that begin to repeat. Because that example,

*
converts come 0.666, a repeating decimal, in i m sorry the 6 repeats infinitely. You would write this together
*
, with a bar over the first decimal digit to indicate that the 6 repeats. Look in ~ this instance of a problem in which 2 consecutive digits in the prize repeat.


Example

Problem

Convert

*
 to a decimal.

*

− 3 3  

70

− 66

40

− 33  

70

− 66

4

0.

*

Using lengthy division, you deserve to see that splitting 4 through 11 results in 0.36 repeating. Together a result, this is written with a line end it as

*
.

Answer

*
 =
*


With numbers better than 1, save the totality number component of the mixed number as the entirety number in the decimal. Then use long department to transform the fraction part to a decimal. For example,

*
 can be created as 2.15.


Example

Problem

Convert

*
 to a decimal.

*

− 8

20

− 20

0

2 + 0.25 = 2.25

Knowing the the entirety number 2 will continue to be the same during the conversion, emphasis only on the decimal part. Using long division, you have the right to see that separating 1 by 4 outcomes in 0.25.

Now bring back the entirety number 2, and also the resulting fraction is 2.25.

Answer

*
 = 2.25


Tips ~ above Converting fractions to Decimals

To write a fraction as a decimal, division the numerator (top) of the fraction by the denominator (bottom) of the fraction.

In the case of repeating decimals, compose the repeating number or digits with a line end it. Because that example, 0.333 repeating would certainly be composed as

*
.

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Summary


Decimal notation is another way to compose numbers the are much less than 1 or that incorporate whole numbers with decimal fractions, sometimes dubbed mixed numbers. Once you compose numbers in decimal notation, you have the right to use an extended place-value graph that has positions because that numbers less than one. You can write numbers created in portion notation (fractions) in decimal notation (decimals), and also you can write decimals together fractions. You can constantly convert in between fractional notation and decimal notation.