Packets  /  Decimals Master
Grades 4-6Elementary

Decimals Master

Place value, comparing, rounding, and all four operations with decimals — plus decimals-fractions-percent conversions and real-world word problems. Learn the concept, practice with instant feedback, and beat the 60-second challenge.

1Decimal Place Value

Key idea: The decimal point separates whole numbers from parts. Each place to the right is one-tenth the place before: tenths, hundredths, thousandths.
  1. Find the decimal point — everything left is whole, everything right is a part of one.
  2. The 1st digit right of the point is tenths (parts of 10).
  3. The 2nd digit is hundredths (parts of 100); the 3rd is thousandths (parts of 1000).
  4. Read the value: in 0.472 the 4 is worth 4/10, the 7 is worth 7/100, the 2 is worth 2/1000.
Worked example
Name the place of each digit in 3.85
3 is in the ones place, 8 is in the tenths place, 5 is in the hundredths place. So 3.85 = 3 ones + 8 tenths + 5 hundredths.
Worked example
What is 0.026 worth?
0 ones, 0 tenths, 2 hundredths, 6 thousandths. As a fraction: 261000, which simplifies to 13500.
Watch out: 0.5 and 0.05 are NOT the same! In 0.5 the 5 is in the tenths place (worth half); in 0.05 it is in the hundredths place (worth a twentieth). Always name the place.

2Comparing Decimals

Key idea: Line up the decimal points and compare digit by digit from left to right — the first place where the digits differ decides which is bigger.
  1. Write both numbers with decimal points lined up.
  2. Pad with zeros so they have the same length (0.7 = 0.70).
  3. Compare ones first, then tenths, then hundredths, moving right.
  4. At the first place where digits differ, the bigger digit wins.
Worked example
Compare 0.7 and 0.65
Pad: 0.70 vs 0.65. Tenths differ: 7 > 6, so the comparison is decided right away. Answer: 0.7 > 0.65.
Worked example
Which is greater: 1.09 or 1.2?
Ones equal (1 = 1); tenths differ: 0 < 2. So 1.09 < 1.2.
Watch out: Longer is NOT bigger! 0.65 < 0.7 even though 65 has more digits than 7. Always pad with zeros before comparing.

3Ordering Decimals

Key idea: To order decimals, pad them to the same length with zeros and sort them like whole numbers.
  1. Line up decimal points and pad each number with zeros to the same length.
  2. Ignore the point and compare the resulting whole numbers.
  3. List them least to greatest (or greatest to least as asked).
  4. Double-check by reading the original decimals.
Worked example
Order 0.4, 0.45, 0.38 from least to greatest
Pad: 0.40, 0.45, 0.38. As whole numbers: 38 < 40 < 45. Order: 0.38, 0.4, 0.45.
Watch out: Do NOT sort by how many digits a number has. 0.38 has two digits but is smaller than 0.4 (one digit).

4Rounding Decimals

Key idea: Find the rounding place, then look at the next digit: 5 or more rounds UP, 4 or less rounds DOWN.
  1. Underline the digit in the rounding place.
  2. Look at the digit immediately to its right.
  3. If it is 5, 6, 7, 8, or 9, round the underlined digit UP.
  4. If it is 0, 1, 2, 3, or 4, keep the underlined digit the same.
  5. Drop everything to the right of the rounding place.
Worked example
Round 0.62 to the nearest tenth
Rounding place is the 6 (tenths). Next digit is 2, which is 4 or less, so round down: 0.6.
Worked example
Round 7.856 to the nearest hundredth
Rounding place is the 5 (hundredths). Next digit is 6, which is 5 or more, so round up: 7.86.
Watch out: Halfway always rounds UP (2.5 rounds to 3). And never round twice — always round from the ORIGINAL number, not from an already-rounded one.

5Adding and Subtracting Decimals

Key idea: LINE UP THE DECIMAL POINTS — then add or subtract exactly like whole numbers and drop the point straight down.
  1. Write the numbers with the decimal points stacked vertically.
  2. Pad with zeros so both have the same number of decimal places.
  3. Add or subtract column by column, carrying or borrowing as usual.
  4. Bring the decimal point straight down into the answer.
Worked example
2.4 + 1.35
Line up: 2.40 + 1.35. Hundredths: 0 + 5 = 5. Tenths: 4 + 3 = 7. Ones: 2 + 1 = 3. Answer: 3.75.
Worked example
5.8 – 2.46
Line up: 5.80 – 2.46. Hundredths: 0 – 6 needs borrow, 10 – 6 = 4. Tenths: 7 – 4 = 3. Ones: 5 – 2 = 3. Answer: 3.34.
Watch out: The #1 mistake is right-aligning the digits instead of the points. 2.4 + 1.35 is NOT 15.9 — the points must line up first.

6Multiplying Decimals

Key idea: Multiply as if there were no decimal points, then place the point: the answer has as many decimal places as the factors COMBINED.
  1. Ignore the decimal points and multiply like whole numbers.
  2. Count the total number of decimal places in ALL factors.
  3. Starting from the right of the product, count back that many places and put the point there.
  4. Add leading zeros if you run out of digits.
Worked example
0.4 x 6
Ignore points: 4 x 6 = 24. Factors have 1 decimal place total. Count back 1: 2.4.
Worked example
1.5 x 1.5
Ignore points: 15 x 15 = 225. Factors have 2 decimal places total. Count back 2: 2.25.
Watch out: 0.4 x 6 = 2.4, NOT 0.24 — count the total decimal places of the factors, not of the answer. And 1.5 x 2 = 3.0 = 3: the decimal can disappear!

7Dividing Decimals

Key idea: When the divisor is a whole number, divide normally and put the decimal point in the answer STRAIGHT UP above the dividend's point.
  1. Set up the long division.
  2. Place the decimal point in the answer directly above the dividend's decimal point.
  3. Divide as with whole numbers.
  4. Add zeros after the decimal point in the dividend if you need to keep going.
Worked example
4.8 / 2
Point goes straight up. 4 / 2 = 2, 8 / 2 = 4. Answer: 2.4.
Worked example
7.2 / 8
Point goes straight up. 7 / 8 = 0 remainder 7; bring down 2: 72 / 8 = 9. Answer: 0.9.
Watch out: With a whole-number divisor, the point goes straight up — do NOT move it. (Dividing by a decimal divisor needs the extra shift step first.)

8Decimals, Fractions, and Percents

Key idea: Decimals, fractions, and percents are three names for the same amount. Read the place value to convert, and remember: percent means 'out of 100'.
  1. Decimal to fraction: read the place value — 0.25 is 25 hundredths = 25100, which simplifies to 14.
  2. Fraction to decimal: write the fraction as tenths or hundredths — 310 = 0.3.
  3. Decimal to percent: multiply by 100 (move the point two places right) and add the % sign — 0.6 = 60%.
  4. Percent to decimal: divide by 100 (move the point two places left) — 75% = 0.75.
Worked example
Convert 0.5
As a fraction: 5 tenths = 510 = 12. As a percent: 0.5 x 100 = 50%. So 0.5 = 12 = 50%.
Worked example
Convert 25%
As a decimal: 25 / 100 = 0.25. As a fraction: 25100 = 14. So 25% = 0.25 = 14.
Watch out: 0.6 is 60%, NOT 6%! Move the point TWO places, not one. And 0.06 is 6% — watch where the 6 sits.
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60-Second Challenge

How many decimals master problems can you solve in 60 seconds?