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Decimal Numbers 3 (Difficult)

Discover how decimals describe speed, sound, and time. This 11 Plus Maths quiz explores the numbers behind how fast sound travels through air.

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Fascinating Fact:

Sound travels through air at about 343.2 metres per second, which is slower than light but fast enough to reach your ears before your brain catches up.

In 11 Plus Maths, decimals help measure speed, distance, and time. They allow scientists to describe movement precisely, from the speed of sound to the timing of echoes.

  • Decimal: A number that uses a point to separate whole numbers from fractions, like 343.2.
  • Speed: The distance an object travels in a set amount of time.
  • Metre per Second: A unit showing how far something moves every second.
How do decimals help measure speed?

Decimals make measurements more exact. For example, 343.2 metres per second is a more accurate value for the speed of sound than simply 343.

Why is sound slower than light?

Sound needs a medium like air or water to travel through, while light can move through empty space. That’s why lightning is seen before thunder is heard.

How do scientists use decimals when studying sound?

Scientists use decimals to record small differences in sound speed, pitch, and echo time, which helps design microphones and musical instruments.

1 .
What was 10.7856 multiplied by if the answer is 107,856?
Ten-thousand
One-thousand
One hundred-thousand
One hundred
The rule for multiplying by a whole number beginning with 1 and followed by one or more zeros, e.g. multiplying by 10, 100, 1,000, ... is as follows: When multiplying by such a number, move the digits to the left by the same number of zeros as in the number: 10,000 × 10.7856 = 107,856: the digits have moved four places to the left = the number of zeros in ten-thousand
2 .
How many grams are there in 2.397 tonnes?
239,700 g
2,397,000 g
23,970 g
2,397 g
There are 1,000 g in 1 kg, and 1,000 kg in 1 tonne. 2.397 x 1,000 x 1,000 = 2,397,000
3 .
What is 103.274 metres in millimetres?
10,327.4 mm
1,032.74 mm
103,274 mm
1,032,740 mm
There are 1,000 mm in 1 m, so in 103.274 m there are 1,000 × 103.274 = 103,274 mm
4 .
What is 235 millimetres in metres?
0.0235 m
23.5 m
2.35 m
0.235 m
There are 1,000 mm in 1 m, so 235 mm ÷ 1,000 = 0.235 m
5 .
A certain object weighs 9.374,808 tonnes. What is this in kilograms?
9,374.808 kg
93,748.08 kg
937.4808 kg
937,480.8 kg
There are 1,000 kg in 1 tonne, so in 9.374,808 tonnes there are 9.374,808 x 1,000 = 9,374.808 kg
6 .
How many cubic centimetres are there in 2.8 cubic metres?
28,000 cm3
2,800,000 cm3
280,000 cm3
2,800 cm3
There are 100 cm in 1 m, so in 1 cubic m there are 100 × 100 x 100 = 1,000,000 cubic cm. In 2.8 cubic m there are 2.8 × 1,000,000 = 2,800,000 cm3
7 .
The Eiffel Tower is 0.324 km tall. How high is it in centimetres?
3,240,000 cm
324,000 cm
32,400 cm
3,240 cm
There are 1,000 m in 1 km, so in 0.324 km there are 0.324 × 1,000 = 324 m.
Next, there are 100 cm in 1 m, so in 324 m there are 324 x 100 = 32,400 cm
8 .
How many grams are there in 26.872 kilograms?
26.872 g
2,687.2 g
268.72 g
26,872 g
There are 1,000 g in 1 kg, so in 26.872 kg there are 1,000 × 26.872 = 26,872 g
9 .
What was 0.00001 multiplied by if the answer is 10?
One thousand
Ten-thousand
One hundred-thousand
One million
For 0.00001 to become 10, the digits will have to move 6 places to the left. You will have to multiply 0.00001 by 1,000,000 - which has 6 zeros
10 .
What was 12,573 divided by if the answer is 0.12573?
One thousand
Ten-thousand
One hundred-thousand
One million
The rule for dividing by a whole number beginning with 1 and followed by one or more zeros, e.g. dividing by 10, 100, 1,000, ... is as follows: When dividing by such a number, move the digits to the right by the same number of zeros as in the number: 12,573 ÷ 100,000 = 0.12573: the digits have moved five places to the right = the number of zeros in one hundred-thousand
Author:  Frank Evans (Specialist 11 Plus Teacher and Tutor)

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