Centos 7 - ping 8.8.8.8 (connect: Network is unreachable)

I think I have a routing problem. I have set up a CentOS VM, it is connected to my network and I can ping other machines.

I cannot however ping anything outside of my network.

[root@localhost ~]# ping 8.8.8.8
connect: Network is unreachable

I also set up port forwarding on my router to forward SSH on port 22 to this machine and I cannot access it outside of my network (using putty).

Here is the output of ip route:

[root@localhost ~]# ip route
10.0.0.0/24 dev enp0s3  proto kernel  scope link  src 10.0.0.10
169.254.0.0/16 dev enp0s3  scope link  metric 1002

Here is the contents of /etc/sysconfig/network-scripts/ifcfg-enp0s3:

TYPE="Ethernet"
BOOTPROTO="static"
IPADDR=10.0.0.10
NETMASK=255.255.255.0
NM_CONTROLLED=no
DEFROUTE="yes"
PEERDNS="yes"
PEERROUTES="yes"
IPV4_FAILURE_FATAL="no"
IPV6INIT="yes"
IPV6_AUTOCONF="yes"
IPV6_DEFROUTE="yes"
IPV6_PEERDNS="yes"
IPV6_PEERROUTES="yes"
IPV6_FAILURE_FATAL="no"
NAME="enp0s3"
UUID="17eeb7fe-f11c-4b8b-83be-a9dd2281dda2"
DEVICE="enp0s3"
ONBOOT="yes"

Based on the errors, you need to update the files to look like this:

/etc/sysconfig/network-scripts/ifcfg-enp0s3:

TYPE="Ethernet"
BOOTPROTO="static"
IPADDR=10.0.0.10
NETMASK=255.255.255.0
NM_CONTROLLED=no
DEFROUTE="yes"
PEERDNS="yes"
PEERROUTES="yes"
IPV4_FAILURE_FATAL="no"
IPV6INIT="yes"
IPV6_AUTOCONF="yes"
IPV6_DEFROUTE="yes"
IPV6_PEERDNS="yes"
IPV6_PEERROUTES="yes"
IPV6_FAILURE_FATAL="no"
NAME="enp0s3"
UUID="17eeb7fe-f11c-4b8b-83be-a9dd2281dda2"
DEVICE="enp0s3"
ONBOOT="yes"

/etc/sysconfig/network:

NETWORKING=yes
HOSTNAME=centos7
GATEWAY=10.0.0.1

/etc/resolv.conf:

nameserver 8.8.8.8
nameserver 8.8.4.4

Add this command:

route add default gw [your gateway IP address]