Lesson 12: Decimal Numbers

New Concept

This course explores the language of mathematics, showing how integers, fractions, decimals, and percents are different ways to represent the same underlying values.

What’s next

We'll begin by focusing on decimal numbers. Next, you’ll see how to read, write, compare, and convert them to fractions and percents.

Property

To read a decimal number, we read the whole number part, say "and" at the decimal point, and then read the fraction part. To read the fraction part of a decimal number we read the digits as though the digits formed a whole number, and then we name the place value of the final digit.

Examples

• 12.05 is read as "twelve and five hundredths" because the last digit, 5, is in the hundredths place.
• 0.125 is read as "one hundred twenty-five thousandths" because the last digit, 5, is in the thousandths place.

Explanation

The decimal point is a separator, like a fence between whole numbers and their fractional parts. For the number to the left, you just read it as usual. When you hit the dot, say 'and.' For the number to the right, read it like a normal number, then finish by naming the place value of the very last digit. It's like giving a number a first and last name!

Property

To express a fraction as a decimal number, we perform the division indicated. For example, to convert $\frac{3}{4}$ to a decimal number, we divide 3 by 4.

Examples

• To convert $\tfrac{3}{8}$, divide $3 \div 8 = 0.375$.
• For a mixed number like $2\tfrac{1}{2}$, the whole number 2 goes before the decimal. Then convert $\tfrac{1}{2}$ by dividing $1 \div 2 = 0.5$. So, $2\tfrac{1}{2} = 2.5$.
• To convert $\tfrac{3}{5}$, divide $3 \div 5 = 0.6$.

Explanation

A fraction is just a division problem in disguise! The fraction bar is a secret 'divided by' sign. To unmask the decimal, you divide the top number (numerator) by the bottom number (denominator). Just add a decimal point and some zeros to the top number to make the long division work out smoothly. Keep going until there's no remainder left over!

Property

To find a percent of a number we change the percent to a decimal or fraction and then multiply. The word 'of' in mathematics usually means to multiply.

Examples

• To find $80\%$ of 40 dollars, convert to a decimal: $0.80 \times 40 = 32$ dollars.
• To find $75\%$ of 40 dollars, convert to a fraction: $\tfrac{3}{4} \times 40 = 30$ dollars.
• To estimate $8\%$ sales tax on 20 dollars: $0.08 \times 20 = 1.60$ dollars.

Explanation

Finding a percentage is like grabbing a specific slice of a whole pie. First, you must convert your percent into a more math-friendly form—either a decimal (by moving the decimal point two spots left) or a fraction. The word 'of' is your secret code word for 'multiply.' So, just multiply your new decimal or fraction by the total number to find your answer!