Question
One day the temperature in Tokyo is $-5^\circ$C and the temperature in Manila is $18^\circ$C .
(a) Work out the difference between these two temperatures
(b) The temperature in Tokyo rises by $4^{\circ}$C.
Find the new temperature in Tokyo.
▶️Answer/Explanation
(a) $23$
(b) $-1$
(a)
Temperature in Tokyo \( -5^\circ \mathrm{C} \)
Temperature in Manila \( 18^\circ \mathrm{C} \)
The difference is
$
18 – (-5)
$
$
18 + 5 = 23^\circ \mathrm{C}
$
(b)
Starting temperature in Tokyo: \( -5^\circ \mathrm{C} \)
Rise in temperature: \( +4^\circ \mathrm{C} \)
$
-5 + 4 = -1^\circ \mathrm{C}
$
Question
(a) Write $164703$ correct to the nearest thousand.
(b) Write $16.983$ correct to l decimal place.
(c) Write $0.037665$ correct to 2 significant figures.
▶️Answer/Explanation
(a) $165 000$ cao
(b) $17.0$ cao
(c) $0.038$ cao
(a)
Look at the hundreds digit (7).
Since 7 is 5 or more, round up the thousands digit.
$164703 \approx 165000$
(b)
Look at the second decimal digit (8).
Since 8 is 5 or more, round up the first decimal place
$16.983 \approx 17.0$
(c)
The first significant figure is 3, and the second is 7.
Look at the next digit (6).
Since 6 is 5 or more, round up the second significant figure.
$0.037665 \approx 0.038$
Question
The temperature at midnight is $-4°C$.
The temperature at noon is $25°C$.
Work out the difference between these two temperatures.
▶️Answer/Explanation
29
Midnight temperature: \(-4^\circ C\)
Noon temperature: \( 25^\circ C \)
The difference between the two temperatures is the distance between them on the number line.
$
25 – (-4) = 25 + 4 = 29^\circ C
$
Question
The temperature on Monday is –27 °C.
The temperature on Tuesday is 15 °C higher than on Monday.
Work out the temperature on Tuesday.
▶️Answer/Explanation
Ans: –12 °C
Monday’s temperature: \( -27^\circ \mathrm{C} \)
Tuesday is 15°C warmer than Monday.
$-27 + 15 = -12^\circ \mathrm{C}$
Question
(a) Write $0.8$ as a fraction.
(b) Write $28\%$ as a decimal.
(c) Write $4876$ correct to the nearest hundred.
▶️Answer/Explanation
Ans:
(a) \(\frac{8}{10}\)
(b) 0.28
(c) 4900
The digit 8 is in the tenths place, so
$
0.8 = \frac{8}{10}
$
Divide both the numerator and denominator by greatest common factor (GCF), which is 2
$
= \frac{8 \div 2}{10 \div 2} = \frac{4}{5}
$
(b)
The percentage symbol (%) means “per hundred,” so \( 28\% \) means 28 out of 100
$
28\% = \frac{28}{100}
$
$
= 0.28
$
(c)
If the tens digit is 5 or more, round up.
If the tens digit is less than 5, round down.
Since the tens digit is 7 (which is 5 or more), we round the hundreds digit up by 1.
Change hundreds digit from 8 to 9.
Set the tens and ones digits to 0.
$
4876 \approx 4900
$
Question
By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of
\(\frac{28.2-5.6}{4.2\times 1.68}\)
You must show all your working.
▶️Answer/Explanation
Ans: \(\frac{30-6}{4\times 2}=3\)
round each number to 1 significant figure and estimate
$
\frac{28.2 – 5.6}{4.2 \times 1.68}
$
\( 28.2 \approx 30 \)
\( 5.6 \approx 6 \)
\( 4.2 \approx 4 \)
\( 1.68 \approx 2 \)
$
\approx \frac{30 – 6}{4 \times 2}
$
$
= \frac{24}{8}
$
$
= 3
$
Question
Write 5926 correct to the nearest 10.
▶️Answer/Explanation
5930
Detailed Solution:
The number is 5926, so the ones digit is 6.
- If the ones digit is 5 or more, round up.
- If the ones digit is 4 or less, round down.
the ones digit is 6 (which is 5 or more), round the number up.
5926 rounded to the nearest 10 becomes 5930.
Question
(a) Write 230 000 in standard form.
(b) Write 4.8 × 10-4 as an ordinary number.
▶️Answer/Explanation
(a)To write 230,000 in standard form, we need to express it as a number multiplied by a power of 10.
Starting with the given number, we count the number of digits to the left of the decimal point, which is 6.
So, we can express 230,000 as \(2.3\times 10^{5}\) in standard form.
(b)To write \(4.8 \times 10^{-4} \)dinary number, we need to evaluate the expression.
The notation \(10^{-4} \)represents the number 1 divided by 10 raised to the power of 4, which is \(\frac{1}{10,000}\)(since \(10^{4}=10,000\))
Therefore,\(4.8\times 10^{-4}\) is equal to 4.8 divided by 10,000:
\(4.8\times 10^{-4}=\frac{4.8}{10000}=0.00048\)
Therefore,\(4.8\times 10^{-4}\) as an ordinary number is 0.00048
Question
A football ground seats 28 750 people when it is full.
(a) Write 28 750 correct to the nearest thousand.
(b) One day 17 250 people attended a football match.
Work out 17 250 as a percentage of 28 750.
▶️Answer/Explanation
(a) To write 28,750 correct to the nearest thousand, we look at the digit in the thousands place and determine whether it should be rounded up or down. In this case, the digit in the thousands place is 8, which is greater than or equal to 5. Therefore, we round up the thousands to the nearest thousand. Thus, 28,750 correct to the nearest thousand is 29,000.
(b) To work out 17,250 as a percentage of 28,750, we divide 17,250 by 28,750 and then multiply by 100 to find the percentage.
\[\frac{17,250}{28,750} \times 100\)
Simplifying the expression:
\(\frac{17,250}{28,750} \times 100 = 0.6 \times 100 = 60\)
Therefore, 17,250 is 60% of 28,750.
Question
Write three hundredths as a decimal.
▶️Answer/Explanation
Three hundredths can be written as 0.03 in decimal form.
Question
(a) Write 326.413 correct to 2 significant figures.
(b) Find the square root of one million.
(c) Calculate
\(\frac{64.3+7.465}{5.2-3.65}.\)
▶️Answer/Explanation
(a) To write 326.413 correct to 2 significant figures, we consider the first two significant figures, which are 3 and 2. The third significant figure, 6, is greater than 5, so we round up the last significant figure. Therefore, 326.413 correct to 2 significant figures is 330.
(b) The square root of one million is 1000. Since one million is equal to 10^6, the square root of one million is equal to 10^(6/2) = 10^3 = 1000.
(c) To calculate \(\frac{64.3+7.465}{5.2-3.65}\), we perform the operations inside the parentheses first:
\(\frac{64.3+7.465}{5.2-3.65} = \frac{71.765}{1.55}\)
Dividing 71.765 by 1.55 gives us:
\(\frac{71.765}{1.55} \approx 46.32\) (rounded to two decimal places)
Therefore, \(\frac{64.3+7.465}{5.2-3.65}\) is approximately 46.32.
Question
Calculate \(\frac{5.27 – 0.93}{4.89 – 4.07}\)
Give your answer correct to 4 significant figures.
▶️Answer/Explanation
To calculate \(\frac{5.27 – 0.93}{4.89 – 4.07}\), we first subtract the numbers in the numerator and denominator:
\(5.27 – 0.93 = 4.34\)
\(4.89 – 4.07 = 0.82\)
\(\frac{4.34}{0.82} \approx 5.29268293\)
To round this result to four significant figures, we consider the fourth digit after the decimal point, which is 6. Since it is greater than 5, we round up the previous digit, which is 9. Therefore, the result becomes:
\(5.293\)
Hence, \(\frac{5.27 – 0.93}{4.89 – 4.07}\) is approximately 5.293 when rounded to four significant figures.