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Decimals: Tenths & Hundredths

Maths · Y4 OC Prep
Year 4 OC
Lesson Guide
Explanation
Decimals continue the place-value pattern past the point: each column is ten times smaller. 3.75 is 3 wholes, 7 tenths, 5 hundredths. You've secretly used decimals for years — money! $3.75 is exactly 3 wholes and 75 hundredths of a dollar. Key conversions: 0.5 = 5/10 = ½, 0.25 = 25/100 = ¼, 0.75 = ¾, 0.1 = 1/10.
Your Turn
Write as decimals: 4 wholes and 3 tenths; and 62/100. Check: 4.3 and 0.62.
Watch Out
0.5 is a HALF, not five. The first digit after the point counts tenths — think 5 tenths.
Explanation
The Year 3 rule 'more digits = bigger' is TRUE for whole numbers and FALSE for decimals — 0.8 beats 0.35! The safe method: pad the shorter one with zeros until lengths match. 0.8 = 0.80, and 80 hundredths beats 35 hundredths. Padding zeros after the point changes nothing (0.8 = 0.80 = 0.800) but makes every comparison honest.
Your Turn
Order largest first: 0.09, 0.4, 0.35. Check: pad → 0.40, 0.35, 0.09.
Watch Out
Pad on the RIGHT of the decimal digits only. 0.8 → 0.80 ✓. Writing 0.08 instead is a different (much smaller) number!
Explanation
Zoom in between whole numbers and ten tenths appear: 2.1, 2.2, up to 2.9. To place 2.7, take 7 small steps past 2 — notice it lands closer to 3 than to 2, which is exactly why 2.7 rounds to 3. OC number-line questions show an arrow between whole numbers and ask which decimal it points to: count the steps, don't eyeball.
Your Turn
Between 5 and 6, which decimal is one step before 6? And which decimal is exactly halfway? Check: 5.9 and 5.5.
Watch Out
Check what one small step is worth first — some OC lines mark twentieths (0.05) or fifths (0.2), not tenths.
Explanation
Adding and subtracting decimals uses the column rules you own: line up the POINTS (not the right-hand ends!), pad the short one with a zero, then work column by column. 3.75 + 1.5: write 1.50, add — 5.25. Money is your built-in checker: $3.75 plus $1.50 is $5.25, obviously. When decimals scare you, put a dollar sign on them.
Your Turn
Work: 2.4 + 1.35, and 5 − 1.2. Check: 3.75; and 5.0 − 1.2 = 3.8.
Watch Out
Whole numbers hide their point: 5 = 5.0. Write it in before subtracting 5 − 1.2, or columns misalign.
Explanation
The final boss: OC mixes fractions and decimals in one question — 'which is largest: 0.7, 3/4, or 0.09?' The plan: convert everything to one costume. As decimals: 0.70, 0.75, 0.09 — so 3/4 wins. Memorise the golden pairs: ½=0.5, ¼=0.25, ¾=0.75, ⅒=0.1, ⅕=0.2 (and its multiples: ⅖=0.4, ⅗=0.6, ⅘=0.8). With those in your pocket, mixed comparisons take seconds. Quiz and exercises — five options, OC style!
Your Turn
Which is smaller: 2/5 or 0.35? Check: 2/5 = 0.40, so 0.35 is smaller.
Watch Out
Pick ONE costume and convert everything — comparing half-converted lists is where errors sneak in.
Step 1: Introduction
Step 1 of 5
The point continues the pattern 3 ones. 7 tenths 5 hundredths 3.75 = 3 wholes + 7 tenths + 5 hundredths. Each column is still ÷10 of the one before: 1 → 0.1 → 0.01. You already know this from money: $3.75 is 3 dollars, 7 ten-cents, 5 cents!
0.8 vs 0.35 — longer isn't bigger! 0.8 > 0.35 Pad to the same length: 0.8 = 0.80. Now compare: 80 vs 35 hundredths. 0.80 > 0.35 — even though "35" has more digits than "8"! Trap: "more digits = bigger" is FALSE for decimals. 0.5 > 0.49 > 0.199 — pad with zeros and the truth appears: 0.500 > 0.490 > 0.199.
Zoom in between the whole numbers 2.0 2.5 3.0 2.7 Between 2 and 3 live ten tenths: 2.1, 2.2, … 2.9. 2.7 sits 7 small steps past 2 — closer to 3 than to 2. Rounding: 2.7 → 3 (nearest whole). 2.5 → 3 (halfway rounds up). OC asks: "which arrow points to 2.7?" — count the small steps!
Line up the points — money style 3.75 + 1.50 5.25 Same rule as always: points under points, pad with zeros. 3.75 + 1.5 → write 1.50 → add columns → 5.25. Sense check with money: $3.75 + $1.50 = $5.25 ✓
One amount, three costumes 1/2 = 0.5 1/4 = 0.25 3/4 = 0.75 1/10 = 0.1 1/5 = 0.2 3/5 = 0.6 OC mixes costumes: "Which is largest: 0.7, 3/4, or 0.09?" Convert to ONE costume: 0.70, 0.75, 0.09 → 3/4 wins. Memorise the six pairs above — they are OC currency.
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