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.