Question

11
there were 1.351×10⁹ metric tons of bananas and 7.49×10⁷ metric tons of grapes produced globally in 2022.
what is the sum of the bananas and grapes produced globally, in metric tons, in 2022? express your answer in scientific notation,
□ × 10□

Explanation:

Step1: Adjust exponents to be equal

To add numbers in scientific notation, we need the same exponent. Rewrite \(1.351\times10^{9}\) as \(13.51\times10^{8}\)? Wait, no. Let's make the exponents the same. \(1.351\times10^{9}=13.51\times10^{8}\)? No, better to make the exponent of the second number \(10^{9}\). \(7.49\times10^{7}=0.749\times10^{8}\)? Wait, no. Wait, \(10^{9}=10\times10^{8}\), \(10^{7}=0.01\times10^{9}\). Wait, let's convert \(7.49\times10^{7}\) to have exponent 9: \(7.49\times10^{7}=0.0749\times10^{9}\). Now add the coefficients: \(1.351 + 0.0749 = 1.4259\)? Wait, no, wait. Wait, \(1.351\times10^{9}=135.1\times10^{7}\). Then add to \(7.49\times10^{7}\): \(135.1 + 7.49 = 142.59\). Then \(142.59\times10^{7}=1.4259\times10^{9}\)? Wait, no. Wait, \(1.351\times10^{9}\) is 1,351,000,000. \(7.49\times10^{7}\) is 74,900,000. Sum: 1,351,000,000 + 74,900,000 = 1,425,900,000. Now convert to scientific notation: 1.4259 × 10⁹. Wait, let's check the steps again.

Step1: Align exponents

Rewrite \(7.49\times10^{7}\) as \(0.749\times10^{8}\)? No, better to have the same exponent. Let's use \(10^{9}\) for both. \(7.49\times10^{7}=7.49\times10^{7}\times10^{2}/10^{2}=749\times10^{5}\)? No, that's not helpful. Wait, correct method: To add \(a\times10^{m}\) and \(b\times10^{n}\) where \(m > n\), convert \(b\times10^{n}\) to \(b\times10^{n - m}\times10^{m}\). So \(m = 9\), \(n = 7\), so \(n - m = -2\). So \(7.49\times10^{7}=7.49\times10^{-2}\times10^{9}=0.0749\times10^{9}\). Now add the coefficients: \(1.351 + 0.0749 = 1.4259\). So the sum is \(1.4259\times10^{9}\). Wait, but let's check by converting to standard form: \(1.351\times10^{9}=1351000000\), \(7.49\times10^{7}=74900000\). Sum: 1351000000 + 74900000 = 1425900000. Now convert 1425900000 to scientific notation: 1.4259 × 10⁹. Yes. So the coefficient is 1.4259 and exponent is 9. Wait, but maybe I made a mistake in the exponent adjustment. Wait, another way: \(1.351\times10^{9}=135.1\times10^{7}\). Then add to \(7.49\times10^{7}\): 135.1 + 7.49 = 142.59. So \(142.59\times10^{7}=1.4259\times10^{9}\) (since 142.59 = 1.4259 × 10², so 1.4259 × 10² × 10⁷ = 1.4259 × 10⁹). Yes, that's correct.

Answer:

1.4259 × 10⁹ (So the first box is 1.4259, the second box is 9)