Decimal Place Value and Conversions
Decimal Place Value
Decimals are another way to represent parts of a whole, using powers of ten instead of arbitrary denominators. The number 0.75 means seventy-five hundredths — exactly the same quantity as the fraction three-fourths, but written in a form that fits naturally into our base-ten number system.
This lesson covers decimal place value, reading and writing decimals, and converting between decimals and fractions. Understanding decimals is critical because they are the standard format for money, measurements, scientific data, and calculator output.
By the end of this lesson you will be able to move fluidly between fractions and decimals, choosing whichever form makes a given problem easier to solve.
Decimals extend the place-value system to the right of the ones place.
| Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|
| 3 | 7 | . | 4 | 0 | 5 |
$37.405$ is read "thirty-seven and four hundred five thousandths."
Each place to the right is one-tenth of the place to its left:
$$1 \to 0.1 \to 0.01 \to 0.001$$
Fraction → Decimal
Divide numerator by denominator.
$\dfrac{3}{8}$ as a decimal.
$3 \div 8 = 0.375$
$\dfrac{1}{3}$ as a decimal.
$0.\overline{3} = 0.333\ldots$
Decimal → Fraction
- Digits after the decimal → numerator.
- Place value of last digit → denominator.
- Simplify.
$0.75$ as a fraction.
$$0.75 = \frac{75}{100} = \frac{3}{4}$$
$0.125$ as a fraction.
$$0.125 = \frac{125}{1000} = \frac{1}{8}$$
Practice Problems
Show Answer Key
1. Hundredths ($0.06$)
2. Forty-seven thousandths
3. $0.875$
4. $\dfrac{9}{25}$
5. $0.833$
6. $3\dfrac{1}{40}$
7. $0.\overline{2}$
8. $\dfrac{1}{125}$
9. $2.75$
10. $\dfrac{5}{8}$
11. $\dfrac{2}{3}$
12. $5.23$