Lesson 1.2: Tenths and Hundredths

New Concept

Explore tenths and hundredths as the foundation of decimals. You'll connect fractions like $\frac{1}{10}$ to their decimal form, $0.1$, learning to convert, compare, and reduce these essential values in various contexts.

What’s next

Next, you’ll work through interactive examples and visual problems. You will master converting between fractions and decimals and apply these skills to new challenges.

Property

Tenths are important fractions because they are the foundation of our decimal number system. We can represent one-tenth in several ways:

• $\frac{1}{10}$ One out of ten
• $0.1$ The first place after the decimal point is the tenths place.
• $0.10$ Ten hundredths is the same as one-tenth: $\frac{10}{100}=\frac{1}{10}$

To find $\frac{1}{10}$ of a number, we divide by 10.

Property

If you can find one-tenth of an amount, you can find two-tenths, or three-tenths, and so on. Remember that $\frac{2}{10}$ can also be written as 0.2, $\frac{3}{10}$ as 0.3, and so on. To find a fraction like $\frac{4}{10}$ (or $0.4$) of a number, first find $\frac{1}{10}$ of the number by dividing by 10, then multiply the result by 4.

Examples

• To find $0.7$ of 420, first find one-tenth: $420 \div 10 = 42$. Then multiply by 7: $42 \times 7 = 294$.
• A park is 90 acres. If $0.3$ of it is woodland, the woodland area is found by first getting $\frac{1}{10}$ of 90, which is 9. Then, $9 \times 3 = 27$ acres.
• Out of 1500 voters, $0.6$ voted for Candidate A. First, $\frac{1}{10}$ is $1500 \div 10 = 150$. So, $150 \times 6 = 900$ people voted for Candidate A.

Explanation

This is a two-step move! First, find the size of one-tenth by dividing. Then, multiply to get the number of tenths you need. It's like grabbing multiple slices of a pizza after you know the size of one slice.

Property

To reduce a fraction, we rewrite it as an equivalent fraction with a smaller denominator. To do this, we divide the numerator and the denominator by the same number. For example, the fraction $\frac{4}{10}$ can be reduced to $\frac{2}{5}$ because both the numerator and denominator are divisible by 2.

Examples

• To reduce the fraction $\frac{9}{12}$, we can divide both the numerator and denominator by 3. This gives $\frac{9 \div 3}{12 \div 3} = \frac{3}{4}$.
• The fraction $\frac{10}{25}$ can be reduced by dividing the top and bottom by 5. This gives $\frac{10 \div 5}{25 \div 5} = \frac{2}{5}$.
• Let's reduce $\frac{24}{32}$. Both numbers are divisible by 8, so we get $\frac{24 \div 8}{32 \div 8} = \frac{3}{4}$.

Explanation

Reducing a fraction is like simplifying a picture. You group smaller pieces into larger, equal-sized ones. The total amount doesn't change, but the fraction becomes easier to understand and work with. It's all about finding the simplest form.

Property

One-tenth of one-tenth is one-hundredth. We write one-hundredth as $\frac{1}{100}$ or $0.01$, with the 1 in the second decimal place, or hundredths place. When we read a decimal fraction, the denominator is given by the place of the last digit.
For example: $0.35 = \frac{35}{100}$ (thirty-five-hundredths).

Examples

• The decimal $0.08$ is read as eight-hundredths and is written as the fraction $\frac{8}{100}$, which can be reduced to $\frac{2}{25}$.
• The decimal $0.65$ represents sixty-five hundredths. As a fraction, it is $\frac{65}{100}$, which reduces to $\frac{13}{20}$.
• The value $0.90$ is ninety-hundredths, or $\frac{90}{100}$. This is equivalent to nine-tenths, or $\frac{9}{10}$.

Explanation

Hundredths are tiny parts, made by splitting one-tenth into 10 more pieces. The second digit after the decimal point shows how many of these tiny hundredth pieces you have. Pay close attention to that second decimal place!

Property

We can find the decimal form for any fraction by dividing the denominator into the numerator. Remember that the fraction bar is really a division symbol. For instance, $\frac{1}{4}$ means "divide one whole into four equal parts," or $1 \div 4 = 0.25$.

Benchmark Fractions as Decimals:

Examples

• To find the decimal form of $\frac{1}{8}$, we calculate $1 \div 8$, which equals $0.125$.
• The decimal form of the fraction $\frac{2}{5}$ is found by dividing 2 by 5, which gives $2 \div 5 = 0.4$.
• For the fraction $\frac{9}{20}$, we perform the division $9 \div 20$, which results in $0.45$.