5th Grade Math Help: Making Decimals Into Fractions or Whole Numbers
In 5th grade, you'll write decimals in an expanded form, which means that you need to be able to change them into fractions. Keep reading to find out how you can change many decimals into fractions or whole numbers.
Changing Decimals to Fractions
All whole numbers and many decimals are rational numbers, which means that they can be written as fractions. In order to do this, you need to understand place values, so let's do a quick review.
Place Values
In a decimal, the whole number part of the amount is shown on the left side of the decimal point. The first number to the left of the decimal point is in the ones place, the second number is in the tens place and the third number is in the hundreds place. The fractional part of the amount is shown on the right side of the decimal. The first number to the right of the decimal point is in the tenths place, the second number is in the hundredths place and the third number is in the thousandths place.
Decimals
Let's start with simple decimals, like 0.4. Since this decimal only has a digit in the tenths place, we can write it as a fraction by putting four over ten, like this: 4/10. Likewise, 0.1 = 1/10, 0.6 = 6/10 and 0.9 = 9/10. For decimals with a digit in the hundredths place, you'll need to drop the decimal point and put the numbers over 100. For instance, 0.42 = 42/100, 0.13 = 13/100 and 0.97 = 97/100. If there's a digit in the thousandths place, you drop the decimal point and put the numbers over 1,000. Practice by writing these decimals as fractions:
1. 0.34
2. 0.2
3. 0.988
Solutions
1. 0.34 = 34/100
2. 0.2 = 2/10
3. 0.988 = 988/1000
Whole Numbers
Some decimals, like 5.0 and 40.0, are already equal to whole numbers. To change a wholenumber decimal to a fraction, put the number as the numerator, and then put one as the denominator. For example, 7.0 = 7/1, 19.0 = 19/1 and 84.0 = 84/1. Complete these practice problems by writing each decimal as a fraction:
1. 9.0
2. 37.0
3. 100.0
Solutions
1. 9.0 = 9/1
2. 37.0 = 37/1
3. 100.0 = 100/1
Mixed Numbers
To write a decimal that's larger than one, like 5.25, as a fraction, you'll need to use mixed numbers. A mixed number is a number that includes a whole number and a fraction, like 3 1/4. The whole number in the decimal becomes the whole number part of the mixed number. For the fraction part of the mixed number, write the digits to the right of the decimal point as a fraction, and then simplify it if necessary. For 5.25, you would change it to 5 25/100, and then simplify to 5 1/4. Practice by changing these decimals to mixed numbers:
1. 1.5
2. 8.75
3. 20.8
Solutions
1. 1.5 = 1 5/10 = 1 1/2
2. 8.75 = 8 75/100 = 8 3/4
3. 20.8 = 20 8/10 = 20 4/5
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Place values and decimal mathematics can be confusing, but the way to master decimals is to first learn how place values work. By learning place values and decimals, your child will be able to better understand the math concepts they will learn in middle and high school.
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