Decimals, Fractions, and Percents: Concepts & Practice

Chapter 1: Key Concepts

• Decimal Place Value and Rounding: Place value tells us the value of each digit in a decimal number. For example, in 3.472, the 4 is in the tenths place, the 7 in the hundredths, and the 2 in the thousandths.
  Rounding means making a number simpler but keeping its value close to what it was (e.g., 4.678 rounded to the nearest tenth is 4.7).
• Changing Fractions to Decimals: Divide the numerator by the denominator. Example: 3/4 = 0.75.
• Changing Decimals to Fractions: Write the decimal as a fraction with the correct place value, then simplify. Example: 0.6 = 6/10 = 3/5.
• Comparing and Ordering Decimals: Line up the decimal points and compare digit by digit from left to right.
• Adding & Subtracting Decimals: Line up the decimal points and add or subtract as usual.
• Adding & Subtracting Money: Treat as decimals (e.g., $3.50 + $2.45).
• Estimating Decimal Sums and Differences: Round decimals to the nearest whole or tenth, then add or subtract.
• Multiplying Decimals & Money: Multiply as whole numbers, then count total decimal places in the factors for the answer.
• Estimating Decimal Products: Round decimals to whole numbers before multiplying.
• Dividing Decimals: For dividing by whole numbers, divide as usual; for dividing by decimals, move the decimal to make the divisor a whole number, and do the same to the dividend.
• Dividing Money: Treat as decimals (e.g., $6.00 ÷ 4 = $1.50).
• Estimating Decimal Quotients: Round numbers before dividing.
• Understanding Percent: Percent means “per 100.” So, 45% means 45 out of 100, or 0.45.
• Percents and Fractions: To turn a percent into a fraction, put it over 100 and simplify. Example: 60% = 60/100 = 3/5.
• Percents and Decimals: To turn a percent into a decimal, divide by 100 or move the decimal point two places left. Example: 8% = 0.08.
• Multiplying Percents and Fractions: Change the percent to a decimal or fraction, then multiply as usual.