Writing Decimals as Fractions (Tenths and Hundredths)
Writing Decimals as Fractions (Tenths and Hundredths) is a Grade 4 math skill from Pengi Math that establishes the direct link between decimal notation and fractions with denominators of 10 or 100. A one-decimal-place number like 0.7 equals 7/10; a two-decimal-place number like 0.43 equals 43/100. Mastering this conversion in 4th grade is essential for understanding place value, comparing decimals, and building toward fraction and decimal operations in Grades 5 and 6.
Key Concepts
Property Decimals can be written as fractions with denominators of 10 or 100. This connection explains why different representations can describe the same value, even though they look different. Tenths (one decimal place): $0.a = \frac{a}{10}$ Hundredths (two decimal places): $0.ab = \frac{ab}{100}$.
Examples 0.6 is the same as $\frac{6}{10}$. 0.4 is the same as $\frac{4}{10}$. 0.30 is the same as $\frac{30}{100}$. 0.75 is the same as $\frac{75}{100}$.
Explanation Decimals are another way to write fractions that have denominators of 10 and 100. The number of digits to the right of the decimal point tells you which denominator to use. One decimal place means the denominator is 10 (tenths), and two decimal places means the denominator is 100 (hundredths). The number itself becomes the numerator of the fraction.
Common Questions
How do you write a decimal as a fraction?
For a decimal with one decimal place (tenths), write the digits after the decimal point over 10. For example, 0.7 = 7/10. For a decimal with two decimal places (hundredths), write the digits after the decimal point over 100. For example, 0.43 = 43/100.
What is 0.6 as a fraction?
0.6 as a fraction is 6/10, because 0.6 means 6 tenths. You can simplify this to 3/5 by dividing both numerator and denominator by 2.
What is 0.25 as a fraction?
0.25 as a fraction is 25/100, because 0.25 means 25 hundredths. This simplifies to 1/4 by dividing both numbers by 25.
Why is the denominator 10 for tenths and 100 for hundredths?
The place value names — tenths and hundredths — directly tell you the denominator. The tenths place means you're counting parts when a whole is split into 10 equal pieces (denominator 10). The hundredths place means the whole is split into 100 equal pieces (denominator 100).
When do 4th graders learn to write decimals as fractions?
4th graders learn this skill in Pengi Math Grade 4 as part of the decimals unit. Understanding the fraction-decimal connection at this level supports comparing, ordering, and computing with decimals in later grades.
How is 0.3 different from 0.30?
0.3 means 3/10 and 0.30 means 30/100. These are equivalent — 3/10 = 30/100 — so 0.3 = 0.30. They represent the same value even though they look different.
Which textbook covers writing decimals as fractions for 4th grade?
Pengi Math Grade 4 covers converting decimals to fractions in the decimals and place value unit, building the foundation for decimal operations and comparison.