Big Whole Numbers
Primary 5 · Mathematics
Big Whole Numbers
Lesson 2 of 3
14 min
Let's begin
It is harvest time, and two cooperatives bring their maize to the store. Uwase's group brings 84,600 kg. Gatete's group brings 84,060 kg.
The two numbers look almost like twins. But one group really did bring more, and everybody wants to know which. Nobody is going to count the grains.
You do not need to. You just need to know how to read the digits.
Compare 99,999 and 100,003.
99,999 has five digits. 100,003 has six. For whole numbers, more digits always wins — a six-digit number is at least 100,000, and a five-digit number can never even reach it.
So 100,003 is the bigger number, and you did not have to compare a single digit.
Back to the maize. Line the two numbers up:
| Number | |||||
|---|---|---|---|---|---|
| 84,600 | 8 | 4 | 6 | 0 | 0 |
| 84,060 | 8 | 4 | 0 | 6 | 0 |
Compare from the left, one place at a time:
So 84,600 is greater than 84,060. Uwase's cooperative brought more maize.
Why does the very first difference settle it? Because that place is worth more than everything to its right put together. Six hundreds beats zero hundreds, and no amount of tens and ones afterwards can catch up.
We write it short: 84,600 > 84,060, or the other way round, 84,060 < 84,600.
The wide open mouth always faces the bigger number. The sharp point always points at the smaller one.
Arrange from smallest to largest: 45,300 405,000 45,030 450,000 40,530
Step 1 — sort them by how many digits they have.
Every five-digit number is smaller than every six-digit number, so the small group goes first.
Step 2 — order the five-digit ones. They all start with 4. Look at the next digit: 5, 5 and 0. The 0 is smallest, so 40,530 comes first. Now compare 45,300 with 45,030: the third digit is 3 against 0, so 45,030 is the smaller.
Step 3 — order the six-digit ones. Both start with 4. Next digit: 0 against 5. So 405,000 is smaller than 450,000.
Answer: 40,530 < 45,030 < 45,300 < 405,000 < 450,000
To go from largest to smallest, just read your list backwards.
Suppose 47 people turned up for umuganda. Is 47 nearer to 40 or to 50?
From 40 up to 47 is 7 steps. From 47 up to 50 is only 3 steps. So 50 is nearer.
Rounded to the nearest ten, 47 becomes 50.
Now try 43: it is 3 steps from 40 and 7 steps from 50, so it rounds down to 40.
And 45? It is stuck exactly in the middle — 5 steps either way. So mathematicians agreed on one rule for everybody: when it is exactly halfway, round up. 45 becomes 50.
Worked example
round 6,382 to the nearest hundred. The hundreds digit is 3. The digit to its right is 8, and 8 is 5 or more, so the 3 climbs to 4. Everything after becomes zero. Answer: 6,400.
Worked example
round 27,451 to the nearest thousand. The thousands digit is 7. The digit to its right is 4, which is less than 5, so the 7 stays. Answer: 27,000. (Do not be tricked by the 5 further along. Only the one digit next door has a vote.)
Worked example
round 348,900 to the nearest ten thousand. The ten thousands digit is 4. Next door is 8, which is 5 or more, so 4 climbs to 5. Answer: 350,000.
Worked example
with a carry — round 79,650 to the nearest thousand. The thousands digit is 9. Next door is 6, so the 9 must go up — but 9 + 1 is 10, so it carries into the next place. 79 thousands become 80 thousands. Answer: 80,000.
At the market Mutesi wants a jerrycan for 3,890 Frw and a basin for 2,120 Frw. She has 6,000 Frw in her hand. Is that enough?
Round each price to the nearest thousand: 3,890 becomes 4,000 and 2,120 becomes 2,000. Together, about 6,000 Frw. That is worryingly close, so she works it out exactly: 3,890 + 2,120 = 6,010 Frw. She is 10 Frw short!
An estimate is a fast answer you can get in your head — and it is also a guard. If you had worked out 3,890 + 2,120 and got 16,010, your estimate of about 6,000 would immediately tell you that something slipped.
Tip
Rounding only ever looks at one digit — the first one after the place you are rounding to. Five or more, send it soar. Four or less, let it rest. Then fill everything behind it with zeros.
When you compare, do the opposite of adding: start on the left, not the right. The first place where the digits differ decides the whole thing.
Put > or < between them: 306,120 and 360,012.
Answer: 306,120 < 360,012. Both have six digits. The first digits match (3 and 3). The next digits are 0 and 6, so 360,012 wins there and wins altogether.
Order from largest to smallest: 70,900 79,000 7,900 90,700.
Answer: 90,700, then 79,000, then 70,900, then 7,900. The last one has only four digits, so it is the smallest. Of the three five-digit numbers, 90,700 starts with 9. Then compare 79,000 and 70,900: the second digit is 9 against 0, so 79,000 is bigger.
Round 5,649 to the nearest hundred.
Answer: 5,600. The hundreds digit is 6, and the digit next door is 4 — less than 5 — so the 6 stays and the rest become zeros.
Round 462,500 to the nearest ten thousand.
Answer: 460,000. The ten thousands digit is 6. The digit next to it is 2 (the thousands digit), which is less than 5, so the 6 stays. The 500 further along has no vote.
Estimate 4,870 + 3,240 by rounding each number to the nearest thousand. Then find the exact answer and see how close you were.
Answer: 4,870 rounds to 5,000 and 3,240 rounds to 3,000, so the estimate is 8,000. The exact sum is 8,110. The estimate is only 110 away — so 8,110 is believable.
What you learned today
Quick check
Which one is true?
