Without using a calculator, arrange the numbers 23, 35, 104 in ascending order. Express your working using powers of 10. 20. Real-life connect: Find the approximate distance from earth to at least 3 planets in km. Express each in standard form and compare.

$$2^3 = 2 \times 2 \times 2 = 8$$ $$3^2 = 3 \times 3 = 9$$ $$5^1 = 5$$ $$10^0 = 1$$

$$10^0 = 1$$ $$5^1 = 5$$ $$2^3 = 8$$ $$3^2 = 9$$

All these values are greater than or equal to $10^0$ and less than $10^1$ (which is 10).

Comparing the values $1, 5, 8, 9$:
$1 < 5 < 8 < 9$
Therefore, the expressions in ascending order are:

$$10^0, 5^1, 2^3, 3^2$$

The expressions in ascending order are $\boxed{10^0, 5^1, 2^3, 3^2}$.

Q20. Real-Life connect: Find the approximate distance from Earth to at least 3 planets in km. Express each in standard form and compare using power of 10.

We will use Mars, Jupiter, and Saturn.

• Approximate average distance from Earth to Mars: 225,000,000 km
• Approximate average distance from Earth to Jupiter: 778,000,000 km
• Approximate average distance from Earth to Saturn: 1,400,000,000 km

Standard form is written as $a \times 10^n$, where $1 \le a < 10$ and $n$ is an integer.

• Mars: $225,000,000 \text{ km} = 2.25 \times 10^8 \text{ km}$
• Jupiter: $778,000,000 \text{ km} = 7.78 \times 10^8 \text{ km}$
• Saturn: $1,400,000,000 \text{ km} = 1.4 \times 10^9 \text{ km}$

To compare, we first look at the exponent of 10. A larger exponent means a larger number.

• Saturn's distance has an exponent of 9 ($10^9$).
• Mars' and Jupiter's distances both have an exponent of 8 ($10^8$).

Since $10^8 < 10^9$, Saturn is farther than both Mars and Jupiter.
To compare Mars and Jupiter, we look at their coefficients because their powers of 10 are the same:
$2.25 < 7.78$.
So, Mars is closer than Jupiter.

The distances in ascending order are:
Mars ($2.25 \times 10^8 \text{ km}$) < Jupiter ($7.78 \times 10^8 \text{ km}$) < Saturn ($1.4 \times 10^9 \text{ km}$).

The approximate distances from Earth to three planets, expressed in standard form and compared, are:

• Mars: $\boxed{2.25 \times 10^8 \text{ km}}$
• Jupiter: $\boxed{7.78 \times 10^8 \text{ km}}$
• Saturn: $\boxed{1.4 \times 10^9 \text{ km}}$ Comparison: $\boxed{\text{Mars} < \text{Jupiter} < \text{Saturn}}$.