To express each of the given numbers in standard form, we will follow these steps:
### Step 1: Diameter of Earth
Given: 12,756,000 m
1. Identify the first non-zero digit: 1 (in 12,756,000).
2. Count the number of places to move the decimal point to the right until we reach the first non-zero digit: 7 places (from 12,756,000 to 1.2756).
3. Write the number in standard form:
\[
12,756,000 = 1.2756 \times 10^7
\]
### Step 2: Distance between Earth and Moon
Given: 384,000,000 m
1. Identify the first non-zero digit: 3 (in 384,000,000).
2. Count the number of places to move the decimal point to the right until we reach the first non-zero digit: 8 places (from 384,000,000 to 3.84).
3. Write the number in standard form:
\[
384,000,000 = 3.84 \times 10^8
\]
### Step 3: Population of India in March 2001
Given: 1,027,000,000
1. Identify the first non-zero digit: 1 (in 1,027,000,000).
2. Count the number of places to move the decimal point to the right until we reach the first non-zero digit: 9 places (from 1,027,000,000 to 1.027).
3. Write the number in standard form:
\[
1,027,000,000 = 1.027 \times 10^9
\]
### Step 4: Number of Stars in a Galaxy
Given: 100,000,000,000
1. Identify the first non-zero digit: 1 (in 100,000,000,000).
2. Count the number of places to move the decimal point to the right until we reach the first non-zero digit: 11 places (from 100,000,000,000 to 1.0).
3. Write the number in standard form:
\[
100,000,000,000 = 1.0 \times 10^{11}
\]
### Step 5: Present Age of Universe
Given: 12,000,000,000 years
1. Identify the first non-zero digit: 1 (in 12,000,000,000).
2. Count the number of places to move the decimal point to the right until we reach the first non-zero digit: 10 places (from 12,000,000,000 to 1.2).
3. Write the number in standard form:
\[
12,000,000,000 = 1.2 \times 10^{10}
\]
### Summary of Answers:
1. Diameter of Earth: \( 1.2756 \times 10^7 \)
2. Distance between Earth and Moon: \( 3.84 \times 10^8 \)
3. Population of India in March 2001: \( 1.027 \times 10^9 \)
4. Number of stars in a galaxy: \( 1.0 \times 10^{11} \)
5. Present age of universe: \( 1.2 \times 10^{10} \)
