Question

about how much energy did china and the united states consume in 2010?
which of these expressions is equivalent to (1 × 10²⁰) + (1 × 10²⁰)?
primary energy consumption
for top 5 countries in 2010
country | energy consumed in 2010 (joules)
china | 1.06 × 10²⁰
u.s. | 1.03 × 10²⁰
russia | 3.09 × 10¹⁹
india | 2.31 × 10¹⁹
japan | 2.30 × 10¹⁹
(1 + 1) × (10²⁰ + 10²⁰)
(1 + 1) × 10²⁰⁺²⁰
(1 + 1) × 10²⁰

Explanation:

Step1: Recall the rule of adding numbers in scientific notation

When adding numbers in scientific notation with the same exponent, we can factor out the power of 10. The general form is \(a\times10^{n}+b\times10^{n}=(a + b)\times10^{n}\).

Step2: Apply the rule to the given expression

We have the expression \((1\times10^{20})+(1\times10^{20})\). Here, \(a = 1\), \(b = 1\) and \(n=20\). So, factoring out \(10^{20}\), we get \((1 + 1)\times10^{20}\).
Let's check the other options:

• Option 1: \((1 + 1)\times(10^{20}+10^{20})\) simplifies to \(2\times(2\times10^{20})=4\times10^{20}\), which is not equivalent to the original expression.
• Option 2: \((1 + 1)\times10^{20 + 20}=(2)\times10^{40}\), which is not equivalent to the original expression.

Answer:

\((1 + 1)\times 10^{20}\)