Unit 3: Decimals & Percents

Concept: What is a Decimal?

A decimal is another way to write a fraction. The decimal point (.) separates the whole number part (on the left) from the fractional part (on the right).

Concept: Place Value

The places to the right of the decimal point represent parts of a whole and end in "-ths".

• The first place is the Tenths place (\(\frac{1}{10}\)).
• The second place is the Hundredths place (\(\frac{1}{100}\)).

I Do: Reading & Writing Decimals

To read a decimal like 6.45, you:

1. Say the whole number: "Six"
2. Say "and" for the decimal point.
3. Say the number after the point: "forty-five"
4. Say the place value of the last digit: "hundredths"

"Six and forty-five hundredths"

Concept: Two Strategies

To compare decimals like 0.8 and 0.65:

1. Line 'Em Up: Write the decimals with their decimal points aligned vertically. Compare digits in each place value from left to right.
2. Annex Zeros: Add zeros to the end of the shorter decimal so they have the same length. Then compare. (e.g., compare 0.80 and 0.65)

I Do: Example

Compare 1.45 and 1.4. Annexing a zero gives us 1.40. Since 45 hundredths is greater than 40 hundredths, 1.45 > 1.4.

Concept: The Golden Rule

The most important rule for adding and subtracting decimals is to line up the decimal points. This ensures that you are adding or subtracting digits with the same place value. You can annex zeros to help line everything up.

I Do: Example

To solve 14.5 + 3.75, you would write it vertically:

  14.50
+  3.75
-------
  18.25

Notice the zero was annexed and the decimal point came straight down.

Concept: What is a Percent?

"Percent" literally means "per one hundred". It's a special fraction where the denominator is always 100.

I Do: Example

If 35 out of 100 squares on a grid are shaded, we can write that as the fraction \(\frac{35}{100}\). Since it's out of 100, this is simply 35%.

Concept: Conversion Rules

• Percent to Decimal: Move the decimal point 2 places to the LEFT (e.g., 75% \(\rightarrow\) 0.75).
• Decimal to Percent: Move the decimal point 2 places to the RIGHT (e.g., 0.5 \(\rightarrow\) 50%).
• Fraction to Decimal: Divide the numerator by the denominator (e.g., \(\frac{1}{4} = 1 \div 4 = 0.25\)).
• Decimal to Fraction: Say it, Write it, Simplify it (e.g., 0.25 is "twenty-five hundredths" \(\rightarrow \frac{25}{100} \rightarrow \frac{1}{4}\)).