KJSEA 2025 Maths Q21 — Place Value & Rounding (10,000 m Race)

KJSEA 2025 Grade 9 Numbers

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The Question

“Anita took part in a 10,000 metre race. She ran 6,784 m and walked the remaining distance. (a) Find the distance she walked. (b) Write 6,784 in words. (c) Round 6,784 to the nearest 100.”

1

Find the distance walked

The whole race is 10,000 metres, made up of the part she ran plus the part she walked. Since we know the total and the running part, we subtract the running distance from the total to get the remaining walked distance.

10000−6784=3216 m10000 - 6784 = 3216 \text{ m}
2

Write the number in words

Read the number by its place values, from the thousands down to the ones. The digit 6 is in the thousands place, 7 in the hundreds, 8 in the tens and 4 in the ones. Grouping these gives the number written out in words.

6784⇒six thousand, seven hundred and eighty-four6784 \Rightarrow \text{six thousand, seven hundred and eighty-four}
3

Identify the rounding digit

To round to the nearest 100 we focus on the hundreds digit, which is 7. Whether it stays or increases is decided by the digit immediately to its right — the tens digit.

67‾84hundreds digit=76\underline{7}84 \quad \text{hundreds digit} = 7
4

Apply the rounding rule

The tens digit is 8. The rule says that if this next digit is 5 or more we round the hundreds digit up, and all digits after it become zero. Because 8 is greater than 5, the hundreds digit goes from 7 up to 8, giving 6,800.

8≥5⇒round up8 \geq 5 \Rightarrow \text{round up}
6784≈68006784 \approx 6800

Final Result

Anita walked 3,216 m. In words, 6,784 is six thousand, seven hundred and eighty-four. Rounded to the nearest 100, 6,784 becomes 6,800.

Why this method works

Each part rests on place value. The total distance is a whole split into two parts, so subtraction recovers the missing part. Writing a number in words is simply naming each digit by the place it occupies. Rounding works the same way: to snap a number to the nearest 100 you keep the hundreds and check the tens digit, because that tens value tells you whether the number is closer to the lower hundred or the higher one. A tens digit of 5 or more means the number is at least halfway to the next hundred, so we move up.

✓

Check: 6,784 + 3,216 = 10,000, confirming the walked distance; and 6,784 is only 16 away from 6,800 but 84 away from 6,700, so 6,800 is the nearer hundred.