Place Value, Ordering & Negative Numbers
Your starting point — no calculator needed
Every digit in a number has a place value. In the number 4 507 213:
4 millions · 5 hundred-thousands · 0 ten-thousands · 7 thousands · 2 hundreds · 1 tens · 3 units
So the 5 is not worth “five” — it is worth 500 000. Place value is how we compare and order numbers.
Decimals work the same way: after the point come tenths, hundredths, thousandths. So 0.7 means 7 tenths — bigger than 0.65 (6 tenths and 5 hundredths).
Negative numbers live to the left of zero on the number line. In Gaborone in July, the temperature can be 25°C in the afternoon and −4°C at night! The further left you go, the smaller the number: −6 is smaller than −2.
The symbols: < means “is smaller than”, > means “is bigger than”. The open (wide) side always faces the bigger number.
What is the value of the digit 5 in 4 507 213?
Count the places from the right: 3 units, 1 tens, 2 hundreds, 7 thousands, 0 ten-thousands, 5 hundred-thousands, 4 millions.
The 5 is worth 500 000.
Order 3.14, 3.41 and 3.104 from smallest to largest.
All start with 3, so compare the tenths: 3.14 and 3.104 have 1 tenth; 3.41 has 4 tenths — so 3.41 is the biggest.
Now compare 3.14 and 3.104 at the hundredths: 3.14 has 4 hundredths, 3.104 has 0 hundredths.
3.104 < 3.14 < 3.41
Longer does not mean bigger — 3.104 has more digits but is the smallest!
One July week in Gaborone, the night temperatures were 2°C, −4°C, 7°C and −1°C. Order them from coldest to warmest.
Put them on the number line. Negatives first — and −4 is further left than −1, so −4 is colder.
−4 < −1 < 2 < 7 — coldest night was −4°C.
Q1. Write down the value of the digit 8 in 3 851 000.
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Q2. Put the correct symbol (< or >) between: 0.7 ☐ 0.65
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0.7 > 0.65 ✓ B1
Q3. Order these from smallest to largest: 5.2 , 5.09 , 5.25
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5.09 < 5.2 < 5.25 ✓ B1
Q4. At dawn in Tsabong the temperature was −3°C. By noon it had risen by 8°C. What was the temperature at noon?
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Q5. Order these from smallest to largest: −6 , 4 , −2 , 0
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−6 < −2 < 0 < 4 ✓ A1
- “Longer means bigger”: 3.104 is NOT bigger than 3.14. Compare place by place from the left — pad with zeros if it helps (3.140 vs 3.104).
- “−6 is bigger than −2 because 6 is bigger than 2”: wrong way round! More negative = smaller. Always picture the number line.
- Giving the digit instead of the value: if asked the value of the 8 in 3 851 000, the answer is 800 000 — not 8.
- Symbol facing the wrong way: the open side of < / > faces the bigger number. Read “−4 < −1” out loud: “minus four is smaller than minus one”. ✓
This Foundation unit prepares you for Core units N-C1 (Types of number) and N-C4 (Fractions, decimals and percentages). In the real IGCSE, ordering questions appear on Papers 1 and 3 — often mixing decimals, fractions and negatives in one list. Master the number line now and those marks are yours later.
(then move on to N-F2 The Four Operations)