1. **Rounding 53 467** (a) To round 53 467 to the nearest 10, look at the units digit (7). Since 7 is 5 or more, round up the tens digit. $$53\,467 \approx 53\,470$$ (b) To round 53 467 to three significant figures, keep the first three digits and round the rest. The first three digits are 5, 3, and 4. The next digit is 6, which is 5 or more, so round up the third digit. $$53\,467 \approx 53\,500$$ (c) To write 53 467 in standard form (scientific notation), express it as a number between 1 and 10 multiplied by a power of 10. $$53\,467 = 5.3467 \times 10^{4}$$ 2. **Using number cards [0.01, 0.1, 1, 10, 100] to satisfy equations:** We need to fill four blanks in: $$24 \times [\ ] = 24 \div [\ ]$$ $$24 \div [\ ] = 24 \times [\ ]$$ - For the first equation, let the cards be $a$ and $b$: $$24 \times a = 24 \div b \implies 24a = \frac{24}{b} \implies ab = \frac{1}{1} = 1$$ So, $a$ and $b$ must multiply to 1. - For the second equation, let the cards be $c$ and $d$: $$24 \div c = 24 \times d \implies \frac{24}{c} = 24d \implies cd = 1$$ So, $c$ and $d$ must also multiply to 1. From the cards, pairs that multiply to 1 are: - $0.1 \times 10 = 1$ - $1 \times 1 = 1$ Since each card can be used only once, the pairs are $0.1$ and $10$. Thus: $$24 \times 0.1 = 24 \div 10$$ $$24 \div 0.1 = 24 \times 10$$ **Final answers:** (a) 53 467 rounded to nearest 10 is $53\,470$. (b) 53 467 rounded to three significant figures is $53\,500$. (c) 53 467 in standard form is $5.3467 \times 10^{4}$. (d) Number cards for equations: $$24 \times 0.1 = 24 \div 10$$ $$24 \div 0.1 = 24 \times 10$$