Question

how many times smaller is $1.2 \times 10^6$ than $1.47 \times 10^7$?
0.82
1.35
2.67
12.25

Explanation:

Step1: Set up the division

To find how many times smaller \(1.2 \times 10^{6}\) is than \(1.47 \times 10^{7}\), we divide \(1.47 \times 10^{7}\) by \(1.2 \times 10^{6}\). So the expression is \(\frac{1.47 \times 10^{7}}{1.2 \times 10^{6}}\).

Step2: Divide the coefficients and the powers of 10 separately

First, divide the coefficients: \(\frac{1.47}{1.2} = 1.225\)? Wait, no, wait. Wait, actually, we want to find how many times smaller \(1.2\times 10^{6}\) is than \(1.47\times 10^{7}\), so it's \(\frac{1.47\times 10^{7}}{1.2\times 10^{6}}\). Let's compute the powers of 10: \(\frac{10^{7}}{10^{6}}=10^{7 - 6}=10^{1} = 10\). Then the coefficients: \(\frac{1.47}{1.2}=1.225\)? Wait, no, wait, maybe I mixed up. Wait, the question is how many times smaller is \(A\) than \(B\), so it's \(B\div A\). So \(B = 1.47\times 10^{7}\), \(A=1.2\times 10^{6}\). So \(\frac{1.47\times 10^{7}}{1.2\times 10^{6}}=\frac{1.47}{1.2}\times\frac{10^{7}}{10^{6}}\). \(\frac{10^{7}}{10^{6}} = 10\), and \(\frac{1.47}{1.2}=1.225\)? Wait, no, 1.47 divided by 1.2: 1.2 times 12.25 is 14.7? Wait, no, 1.2 times 12.25 is 14.7? Wait, 1.47 / 1.2: multiply numerator and denominator by 100 to get 147/120 = 49/40 = 1.225? Wait, but the options don't have 1.225. Wait, maybe I made a mistake. Wait, wait, the question is how many times smaller is \(1.2\times 10^{6}\) than \(1.47\times 10^{7}\), so it's \(1.47\times 10^{7}\div(1.2\times 10^{6})\). Let's compute that:

\(1.47\times 10^{7}=14700000\), \(1.2\times 10^{6}=1200000\). Then \(14700000\div 1200000 = 147\div 12 = 12.25\)? Wait, that can't be. Wait, no, wait, 1.47×10⁷ is 14,700,000 and 1.2×10⁶ is 1,200,000. So 14,700,000 ÷ 1,200,000 = 147 ÷ 12 = 12.25? But the options have 12.25? Wait, the options are 0.82, 1.35, 2.67, 12.25? Wait, the last option is 12.25? Wait, the user's image shows 12.25 as an option. Oh, I see, I miscalculated earlier. Let's do it again:

\(\frac{1.47\times 10^{7}}{1.2\times 10^{6}}=\frac{1.47}{1.2}\times\frac{10^{7}}{10^{6}}\). \(\frac{10^{7}}{10^{6}} = 10\), and \(\frac{1.47}{1.2}=1.225\)? No, 1.47 divided by 1.2: 1.2 × 12.25 = 14.7, so 1.47 / 1.2 = 1.225? Wait, no, 1.2 × 12.25 = 14.7, so 1.47 / 1.2 = 1.225? But 1.225 × 10 = 12.25. Ah, there we go. So 1.225 × 10 = 12.25. So the answer is 12.25, which is one of the options (the last one: 12.25).

Wait, let's check again:

\(1.47\times 10^{7}=14700000\)

\(1.2\times 10^{6}=1200000\)

Now, divide 14700000 by 1200000:

14700000 ÷ 1200000 = (14700000 ÷ 100000) ÷ (1200000 ÷ 100000) = 147 ÷ 12 = 12.25. Yes, that's correct. So the answer is 12.25, which is the last option.

Answer:

12.25 (the option with 12.25)