Decimal fraction facts for kids

Decimal fractions are special kinds of rational numbers. They are numbers that can be written as a fraction where the bottom part (the denominator) is a power of ten. Powers of ten are numbers like 10, 100, 1,000, and so on.

For example, the decimal number 0.8 can be written as the fraction 8/10. The number 14.89 can be written as 1489/100. And 0.00079 is the same as 79/100000. All these are decimal fractions because their denominators are powers of ten.

However, not all fractions can be written as a decimal fraction with a limited number of digits. For instance, 1/3 (one-third) cannot be written as a decimal fraction with a finite number of digits because 3 is not a power of 10. If you try to divide 1 by 3, you get 0.3333... which goes on forever.

When a number has a certain number of digits after the decimal point, it means its fraction form has a denominator that is a power of ten. For example, if there are n digits after the decimal point, the denominator will be 10 raised to the power of n (10ⁿ). You can find the top part (the numerator) by simply removing the decimal point from the number.

This means a number is a decimal fraction if it can be written with a limited number of digits after the decimal point.

When you simplify decimal fractions as much as possible, their denominators will always be made up of only 2s and 5s multiplied together. For example, 10 is 2 times 5. 100 is 2 times 2 times 5 times 5. Here are some of the smallest denominators for decimal numbers:

• 1 (which is 2⁰ × 5⁰)
• 2 (which is 2¹ × 5⁰)
• 4 (which is 2² × 5⁰)
• 5 (which is 2⁰ × 5¹)
• 8 (which is 2³ × 5⁰)
• 10 (which is 2¹ × 5¹)
• 16 (which is 2⁴ × 5⁰)
• 20 (which is 2² × 5¹)
• 25 (which is 2⁰ × 5²)

Why are Decimal Numbers Important?

Decimal numbers are super useful even though they can't show every single real number perfectly. Think about pi (π), which is a number that goes on forever without repeating. We often use 3.14159 as a decimal approximation for pi. This decimal is very close to the real value, being off by less than 10⁻⁵ (which is 0.00001).

Because they can get very close to any real number, decimals are used everywhere! You'll find them in science, engineering, and in your daily life.

How Decimals Help with Measurements

When we measure things, there's always a little bit of measurement uncertainty. This means our measurement might not be exactly perfect. Decimal numbers are great for showing how accurate a measurement is.

For example, if you see a measurement written as 0.080, it suggests that the error in the measurement is less than 0.001. If it's written as 0.08, it means the error is less than 0.01. Even though 0.080 and 0.08 represent the same number, the extra zero in 0.080 tells us that the measurement was taken with more precision. The actual value could be something like 0.0803 or 0.0796.

This is why you often see measurements with a certain number of digits after the decimal point. Those digits tell you how precise the measurement is.