Question

in 2003 approximately 80,400,000 pounds of blueberries were harvested in the united states. what is the value of the digit \4\ in that number? the groundhog must feed her young so they can grow and be healthy. if she brings forty - five berries back to the burrow to feed her young and they only eat two - thirds of them, how many berries did they eat? nathan was looking on the internet for information about dinosaurs. the search engine brought up 13 pages of web sites. if there were 12 web sites on each page, how many web sites were there in all?

Explanation:

First Sub - Question:

Step1: Identify the place of digit 4

The number is 80,400,000. Let's write the number in place - value form. The places from right to left are: ones, tens, hundreds, thousands, ten - thousands, hundred - thousands, millions, ten - millions. In 80,400,000, the digit 4 is in the hundred - thousands place? Wait, no. Wait, 80,400,000 can be written as \(8\times10^{7}+0\times10^{6}+4\times10^{5}+0\times10^{4}+0\times10^{3}+0\times10^{2}+0\times10^{1}+0\times10^{0}\)? Wait, no. Wait, 80,400,000: let's count the digits. The number is 80400000. Let's separate the digits: 8 (ten - millions place), 0 (millions place), 4 (hundred - thousands place)? Wait, no. Wait, 80,400,000. Let's write it as 80 million 400 thousand. So the digit 4 is in the hundred - thousands place? Wait, no. Wait, 80,400,000: the places are:

• The right - most digit is the 0th place (units).
• Moving left: 1st place (tens), 2nd (hundreds), 3rd (thousands), 4th (ten - thousands), 5th (hundred - thousands), 6th (millions), 7th (ten - millions).

So 80,400,000 is written as:

\(8\times10^{7}+0\times10^{6}+4\times10^{5}+0\times10^{4}+0\times10^{3}+0\times10^{2}+0\times10^{1}+0\times10^{0}\)

Wait, no. Wait, 80,400,000: let's count the digits. The number is 8 0 4 0 0 0 0 0. So the first digit (left - most) is 8 (10,000,000 place, i.e., \(10^{7}\)), then 0 (\(10^{6}\)), then 4 (\(10^{5}\)), then 0 (\(10^{4}\)), then 0 (\(10^{3}\)), then 0 (\(10^{2}\)), then 0 (\(10^{1}\)), then 0 (\(10^{0}\)).

Wait, \(10^{5}\) is 100,000. So \(4\times10^{5}=400,000\). Wait, but 80,400,000: 80 million is 80,000,000 and 400,000 is 400,000. So 80,000,000+400,000 = 80,400,000. So the digit 4 is in the hundred - thousands place? Wait, no. Wait, 100,000 is hundred - thousand. So \(4\times100,000 = 400,000\). Wait, but maybe I made a mistake. Wait, 80,400,000: the digit 4 is in the hundred - thousands place? Wait, no. Wait, 80,400,000 is 80 million 400 thousand. So 400 thousand is \(4\times100,000=400,000\). So the value of the digit 4 is 400,000.

Wait, let's re - express the number: 80,400,000. Let's write it as 80400000. The digit 4 is at the 5th position from the right (since we start counting from 0). The place value of a digit in the \(n\)th position (from the right, starting at 0) is \(digit\times10^{n}\).

The digit 4 is at the 5th position (since positions are 0 - 7: 0 (units), 1 (tens), 2 (hundreds), 3 (thousands), 4 (ten - thousands), 5 (hundred - thousands), 6 (millions), 7 (ten - millions)). So \(n = 5\), digit = 4. So the value is \(4\times10^{5}=400,000\).

Step2: Confirm the place value

The number 80,400,000. Let's break it down:

• 8 is in the ten - millions place: \(8\times10,000,000 = 80,000,000\)
• 0 is in the millions place: \(0\times1,000,000 = 0\)
• 4 is in the hundred - thousands place: \(4\times100,000 = 400,000\)
• The rest of the digits are 0.

So the value of the digit 4 is 400,000.

Step1: Identify the number of berries brought

The groundhog brings 45 berries.

Step2: Calculate the number of berries eaten

The young eat two - thirds of the berries. So we need to find \(\frac{2}{3}\) of 45.

The formula for finding a fraction of a number is \(number\times fraction\). So we calculate \(45\times\frac{2}{3}\).

\(45\div3 = 15\), and \(15\times2=30\).

Step1: Identify the number of pages and sites per page

There are 13 pages, and 12 websites per page.

Step2: Calculate the total number of websites

To find the total number of websites, we multiply the number of pages by the number of websites per page. So we calculate \(13\times12\).

\(13\times12=(10 + 3)\times12=10\times12+3\times12 = 120+36 = 156\).

Answer:

400000

Second Sub - Question: