Numbers can be expressed in different ways, and that can be a tricky concept for kids. Read on to learn how to teach kids to convert a decimal to fraction and a fraction to decimal.
How to Convert Numbers
Fractions and decimals are two sides of the same coin; they both express parts of a whole. Each form has its advantages. Decimals are easier to compare to one another since they all operate on a base-10 system. Which number is greater: 0.5 or 0.3? It’s easy to spot. The place values of decimals are all multiples of 1/10: tenths, hundredths, thousandths, and so on.
Fractions have the upper hand when it comes to expressing a precise value. For example, ⅓ is a precise amount, but when you try to show that with a decimal, you get 0.333…where the 3 repeats infinitely. Although you can express ⅓ as a decimal, you can’t add, subtract, multiply, or divide that decimal exactly.
Learning to move back and forth between decimals and fractions helps first with measurements, but it’s a skill you use consistently in higher-level mathematics like algebra and geometry.
Decimal to Fraction
When you are teaching kids to convert numbers, you want to start with decimal to fraction conversion; it’s easier. First, you teach kids about place value. If they can look at 0.5 and tell you that is “five tenths,” you are halfway home.
Start with decimals in the tenths place and have the student say the value out loud. When a student reads 0.3 as “three tenths,” ask her how to write three tenths as a fraction: 3/10.
Practice this technique with decimals in the hundredths and thousandths place as well. Remember, all decimals will be converted to fractions with denominators that are powers of 10: 10, 100, 1000, etc.
Once you have converted a decimal to a fraction, you may need to simplify the fraction. For example, 0.5 is “five tenths.” As a fraction, that is 5/10. This is not the simplest way to write that fraction, since both the numerator and the denominator (the top and bottom numbers) can be divided by 5. 5/10 can be simplified to ½.
Practice giving the student decimals whose equivalent fractions can be simplified. For example, 0.48 is 48/100, which can be simplified to 12/25.
Fraction to Decimal
When you are teaching students to convert a fraction to decimal, they must already know how to do long division. Start by showing the students the four ways to write a division symbol. No doubt they can easily identify ÷ and the division bar ⟌. But do they know that the fraction bars such as — and / are also division symbols?
Write 10 ➗ 2 and have the student say out loud “10 divided by 2.” Write it with a division bar as well 2⟌10 and have the student repeat “10 divided by 2.” Then write 10/2 and have the student read it the same way: “10 divided by 2.” Practice writing division problems with all four division symbols until the student understands that they all mean the same thing.
Once that clicks, the student is ready to understand that any fraction is basically a division problem. ½ is really “1 divided by 2.” Although that may seem impossible at first, you can divide a smaller number by a larger one when you use long division. You simply need to use decimals to extend the number. “1 divided by 2” becomes 2⟌1.0. As long as the student knows how to divide with decimals, he will be able to come up with the answer: 0.5.
Converting Decimal to Fraction and Fraction to Decimal
Decimals and fractions are basically the same things. Each represents part of a whole number. Both forms have their advantages, so knowing how to convert one to another is a handy skill that will strengthen your student’s math ability. Once your students have mastered place value and long division with decimals, you can easily teach them how to convert decimal to fraction and fraction to decimal.