Math / Numbers & Operations

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In 1500 CE , the world's population was about $4.5 \times 10^{8}$ . In 2020, the world's population was about $7.8 \times 10^{9}$ . Find how much the world's population increased. (1 point) $12.3 \times 10^{9}$ $8.25 \times 10^{9}$ $3.3 \times 10^{9}$ $7.35 \times 10^{9}$ Check answer Remaining Attempts: 3

Studdy Solution

STEP 1

What is this asking? We need to find the difference in world population between the year 2020 and the year 1500. Watch out! The populations are written using scientific notation, so we need to be careful with our calculations!

STEP 2

1. Convert to same exponent
2. Calculate the difference

STEP 3

To subtract numbers in scientific notation, the exponents need to be the same.
This allows us to factor out the common power of 10.

STEP 4

Let's convert the population in 1500 to have an exponent of 9, just like the population in 2020.

STEP 5

The 1500 population is $4.5 \cdot 10^8$ .
To increase the exponent by 1, we need to divide the coefficient by 10.
So, $4.5 \cdot 10^8$ becomes $(4.5 \div 10) \cdot 10^{8+1}$ , which simplifies to $0.45 \cdot 10^9$ .

STEP 6

Now we can subtract the 1500 population ( $0.45 \cdot 10^9$ ) from the 2020 population ( $7.8 \cdot 10^9$ ).

STEP 7

$(7.8 - 0.45) \cdot 10^9$ This gives us: $7.35 \cdot 10^9$

STEP 8

The world population increased by $7.35 \cdot 10^9$ people.

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Studdy Solution

STEP 1

What is this asking? We need to find the difference in world population between the year 2020 and the year 1500. Watch out! The populations are written using scientific notation, so we need to be careful with our calculations!

STEP 2

1. Convert to same exponent
2. Calculate the difference

STEP 3

To subtract numbers in scientific notation, the exponents need to be the same.
This allows us to factor out the common power of 10.

STEP 4

Let's convert the population in 1500 to have an exponent of 9, just like the population in 2020.

STEP 5

The 1500 population is $4.5 \cdot 10^8$ .
To increase the exponent by 1, we need to divide the coefficient by 10.
So, $4.5 \cdot 10^8$ becomes $(4.5 \div 10) \cdot 10^{8+1}$ , which simplifies to $0.45 \cdot 10^9$ .

STEP 6

Now we can subtract the 1500 population ( $0.45 \cdot 10^9$ ) from the 2020 population ( $7.8 \cdot 10^9$ ).

STEP 7

$(7.8 - 0.45) \cdot 10^9$ This gives us: $7.35 \cdot 10^9$

STEP 8

The world population increased by $7.35 \cdot 10^9$ people.

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Studdy Solution

STEP 1

What is this asking? We need to find the difference in world population between the year 2020 and the year 1500. Watch out! The populations are written using scientific notation, so we need to be careful with our calculations!

STEP 2

1. Convert to same exponent2. Calculate the difference

STEP 3

To subtract numbers in scientific notation, the exponents need to be the same.This allows us to factor out the common power of 10.

STEP 4

Let's convert the population in 1500 to have an exponent of 9, just like the population in 2020.

STEP 5

The 1500 population is 4.5⋅1084.5 \cdot 10^84.5⋅108.To increase the exponent by 1, we need to divide the coefficient by 10.So, 4.5⋅1084.5 \cdot 10^84.5⋅108 becomes (4.5÷10)⋅108+1(4.5 \div 10) \cdot 10^{8+1}(4.5÷10)⋅108+1, which simplifies to 0.45⋅1090.45 \cdot 10^90.45⋅109.

STEP 6

Now we can subtract the **1500 population** (0.45⋅1090.45 \cdot 10^90.45⋅109) from the **2020 population** (7.8⋅1097.8 \cdot 10^97.8⋅109).

STEP 7

(7.8−0.45)⋅109(7.8 - 0.45) \cdot 10^9(7.8−0.45)⋅109 This gives us: 7.35⋅1097.35 \cdot 10^97.35⋅109

STEP 8

The world population increased by 7.35⋅1097.35 \cdot 10^97.35⋅109 people.

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Studdy solves anything!

Start learning now

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1. Convert to same exponent
2. Calculate the difference

To subtract numbers in scientific notation, the exponents need to be the same.
This allows us to factor out the common power of 10.

The 1500 population is $4.5 \cdot 10^8$ .
To increase the exponent by 1, we need to divide the coefficient by 10.
So, $4.5 \cdot 10^8$ becomes $(4.5 \div 10) \cdot 10^{8+1}$ , which simplifies to $0.45 \cdot 10^9$ .

Now we can subtract the 1500 population ( $0.45 \cdot 10^9$ ) from the 2020 population ( $7.8 \cdot 10^9$ ).

$(7.8 - 0.45) \cdot 10^9$ This gives us: $7.35 \cdot 10^9$

The world population increased by $7.35 \cdot 10^9$ people.